Question

the width of a rectangle is 25% of the length. the perimeter is 310 cm. find the length and width of the rectangle. length cm width cm

Explanation:

Step1: Define variables

Let the length of the rectangle be $l$ cm and the width be $w$ cm. Given $w = 0.25l$.

Step2: Use perimeter formula

The perimeter formula of a rectangle is $P=2(l + w)$. Substitute $P = 310$ and $w = 0.25l$ into it: $310=2(l + 0.25l)$.

Step3: Simplify the equation

First, simplify the right - hand side: $l+0.25l = 1.25l$, so the equation becomes $310 = 2\times1.25l=2.5l$.

Step4: Solve for length $l$

Divide both sides of the equation $310 = 2.5l$ by 2.5: $l=\frac{310}{2.5}=124$ cm.

Step5: Solve for width $w$

Since $w = 0.25l$, substitute $l = 124$ into it: $w=0.25\times124 = 31$ cm.

Answer:

length: 124 cm
width: 31 cm